考かんがえ抜ぬく

godan verb (-ku)

think through; think thoroughly; think hard

Implies deep, exhaustive thinking until a conclusion is reached. Often used when solving a problem or making a decision after careful consideration.

• 一ひと晩ばん中じゅう考かんがえ抜ぬいて、やっと答こたえが出でた。

  I thought it through all night and finally found the answer.

• この問もん題だいを考かんがえ抜ぬくには時じ間かんがかかる。

  It takes time to think this problem through thoroughly.